Physicist and chemical engineering professor Sharon Glotzer and her collaborators in the research, Michael Engel and Pablo Damasceno, recognized—along with others—that nanoparticles with certain geometries have a greater tendency to organize themselves into structures when they were crowded together. From this observation they wondered if nanoparticles with other geometries would do the same.

"We studied 145 different shapes, and that gave us more data than anyone has ever had on these types of potential crystal-formers," Glotzer says in the university press release covering the research. "With so much information, we could begin to see just how many structures are possible from particle shape alone, and look for trends."

It might be better to think of entropy as a tendency toward equilibrium rather than disorder. This might help better describe how entropy aids the nanoparticles in self-assembling into structures.

To clarify this, Glotzer urges a remake of entropy’s image in the press release. In her explanation, entropy is a measure of possibilities. To describe how this measure of possibilities influences the nanoparticles, Glotzer says to imagine the nanoparticles as a bag of dice being emptied into a jar where there is no gravity. Based on entropy, the dice would find themselves dispersed throughout the jar. However, when you put enough dice into the jar—and they run out of space—they begin to align themselves.

According to the University of Michigan team's simulations, this metaphorical description holds true as well for the nanoparticles. The nanoparticles are so small that the forces of gravity have less of an impact on them than does this property of entropy.

"It's all about options. In this case, ordered arrangements produce the most possibilities, the most options. It's counterintuitive, to be sure," Glotzer says in the release.

What the simulation demonstrated was that by knowing the geometry of the nanoparticles, you can predict the kind of structure they will form.

One of the unresolved mysteries from the simulation the researchers observed is that around 30 percent of the nanoparticles never form into a more complex structure. Why this is the case, they are not sure.

"These may still want to form crystals but got stuck. What's neat is that for any particle that gets stuck, we had other, awfully similar shapes forming crystals," Glotzer said.